Stabilised Hybrid Discontinuous Galerkin Methods for the Stokes Problem with Non-standard Boundary Conditions

摘要

In this work we have applied the idea introduced in [10] to stabilise the hdG method proposed in [1] for the Stokes problem with TVNF boundary conditions. The method adds a simple, symmetric, term to the formulation, and allowed us to use a higher order pressure space, which, in turn, improved the pressure convergence (although a proof of this fact is, in general, not available). This approach was also applied to NVTF boundary conditions (see [6]) and can be used for other discontinuous Galerkin methods that deal with Stokes or nearly incompressible elasticity problems.